Why is my mesh inversed when Imported to Unity?
One possible reason for this could be that the normals actually were inverted in Blender but if you have Backface Culling disabled then the mesh could look right even though it's not.  The lighting may look weird but the polygons will look like they are facing outwards.



Backface culling is an optimization that disables shading on polygons that are not supposed to ever be seen.  

When in Edit Mode, you can activate a tool that will show you which direction the normals are pointing in.  Just make sure that the size is adjusted appropriately for the model's scale otherwise you may not see them.



To correct the normals, you can use Ctrl+n which is also shown in the following image as a toolbar button labeled Recalculate.  

You can also selectively flip the direction of faces using the button labeled Flip Direction which can also be located in the Faces Menu Ctrl+f with the alternate name Flip Faces 



(The different names are a mistake, both use bpy.ops.mesh.flip_normals())